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Let us now consider a reallife damping mechanism. Equation (464)
specifies the linearized Ohm's law in the collisionless
coldplasma approximation.
However, in the presence of collisions this expression acquires
an extra term (see Sect. 3), such that

(614) 
where
is the collision frequency. Here,
we have neglected the small difference between the parallel and perpendicular
plasma electrical conductivities, for the sake of simplicity. When
Eq. (614) is used to calculate the dielectric permittivity for a
righthanded wave, in the limit
, we obtain

(615) 
A righthanded circularly polarized wave, propagating parallel to the
magnetic field, is governed by the dispersion relation

(616) 
Suppose that . Furthermore, let

(617) 
so that the electron cyclotron resonance is located at .
We also assume that
, so that the evanescent region
corresponds to .
It follows that in the immediate vicinity of the resonance

(618) 
where

(619) 
and

(620) 
It can be seen that , which is consistent with the
absorption of incident wave energy by the resonant layer. The
approximate width of the resonant layer
is

(621) 
Note that the damping mechanism, in this case collisions, controls the
thickness of the resonant layer, but does not control the
amount of wave energy absorbed by the layer. In fact, in the simple
theory outlined above,
all of the incident wave energy is absorbed by the layer.
Next: Pulse Propagation
Up: Waves in Cold Plasmas
Previous: Resonant Layers
Richard Fitzpatrick
20110331